Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.32143 | −1.34028 | −0.670140 | − | 0.742235i | \(-0.733766\pi\) | ||||
−0.670140 | + | 0.742235i | \(0.733766\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.515797 | 0.194953 | 0.0974765 | − | 0.995238i | \(-0.468923\pi\) | ||||
0.0974765 | + | 0.995238i | \(0.468923\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.38904 | 0.796348 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.54079 | 1.36910 | 0.684550 | − | 0.728966i | \(-0.259999\pi\) | ||||
0.684550 | + | 0.728966i | \(0.259999\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.42147 | 0.394244 | 0.197122 | − | 0.980379i | \(-0.436841\pi\) | ||||
0.197122 | + | 0.980379i | \(0.436841\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.32143 | 0.599391 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.21357 | 0.779406 | 0.389703 | − | 0.920941i | \(-0.372578\pi\) | ||||
0.389703 | + | 0.920941i | \(0.372578\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.56977 | −0.589546 | −0.294773 | − | 0.955567i | \(-0.595244\pi\) | ||||
−0.294773 | + | 0.955567i | \(0.595244\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.19739 | −0.261291 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.925577 | −0.192996 | −0.0964981 | − | 0.995333i | \(-0.530764\pi\) | ||||
−0.0964981 | + | 0.995333i | \(0.530764\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.41829 | 0.272950 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.44774 | −0.268839 | −0.134420 | − | 0.990925i | \(-0.542917\pi\) | ||||
−0.134420 | + | 0.990925i | \(0.542917\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.16275 | −1.10686 | −0.553431 | − | 0.832895i | \(-0.686682\pi\) | ||||
−0.553431 | + | 0.832895i | \(0.686682\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.5411 | −1.83498 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.515797 | −0.0871856 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.88040 | −0.966732 | −0.483366 | − | 0.875418i | \(-0.660586\pi\) | ||||
−0.483366 | + | 0.875418i | \(0.660586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.29984 | −0.528397 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.02106 | −1.40885 | −0.704426 | − | 0.709777i | \(-0.748796\pi\) | ||||
−0.704426 | + | 0.709777i | \(0.748796\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.54662 | −1.15085 | −0.575424 | − | 0.817855i | \(-0.695163\pi\) | ||||
−0.575424 | + | 0.817855i | \(0.695163\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.38904 | −0.356138 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.06959 | −0.156016 | −0.0780082 | − | 0.996953i | \(-0.524856\pi\) | ||||
−0.0780082 | + | 0.996953i | \(0.524856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.73395 | −0.961993 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.46009 | −1.04462 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.39722 | 0.466644 | 0.233322 | − | 0.972400i | \(-0.425040\pi\) | ||||
0.233322 | + | 0.972400i | \(0.425040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.54079 | −0.612280 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.96555 | 0.790156 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.53271 | 1.11086 | 0.555432 | − | 0.831562i | \(-0.312553\pi\) | ||||
0.555432 | + | 0.831562i | \(0.312553\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.29821 | 0.550330 | 0.275165 | − | 0.961397i | \(-0.411268\pi\) | ||||
0.275165 | + | 0.961397i | \(0.411268\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.23226 | 0.155250 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.42147 | −0.176311 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.75453 | −0.947367 | −0.473683 | − | 0.880695i | \(-0.657076\pi\) | ||||
−0.473683 | + | 0.880695i | \(0.657076\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.14866 | 0.258669 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.31767 | 0.868448 | 0.434224 | − | 0.900805i | \(-0.357023\pi\) | ||||
0.434224 | + | 0.900805i | \(0.357023\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.48265 | 0.758737 | 0.379368 | − | 0.925246i | \(-0.376141\pi\) | ||||
0.379368 | + | 0.925246i | \(0.376141\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.32143 | −0.268056 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.34213 | 0.266910 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.18911 | 0.696330 | 0.348165 | − | 0.937433i | \(-0.386805\pi\) | ||||
0.348165 | + | 0.937433i | \(0.386805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.4596 | −1.16218 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 16.0002 | 1.75625 | 0.878125 | − | 0.478432i | \(-0.158795\pi\) | ||||
0.878125 | + | 0.478432i | \(0.158795\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.21357 | −0.348561 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.36084 | 0.360319 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.5007 | 1.43108 | 0.715538 | − | 0.698574i | \(-0.246182\pi\) | ||||
0.715538 | + | 0.698574i | \(0.246182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.733188 | 0.0768590 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.3064 | 1.48350 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.56977 | 0.263653 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.67511 | 0.779289 | 0.389645 | − | 0.920965i | \(-0.372598\pi\) | ||||
0.389645 | + | 0.920965i | \(0.372598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.8482 | 1.09028 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15.5710 | −1.54938 | −0.774688 | − | 0.632343i | \(-0.782093\pi\) | ||||
−0.774688 | + | 0.632343i | \(0.782093\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.28758 | −0.323934 | −0.161967 | − | 0.986796i | \(-0.551784\pi\) | ||||
−0.161967 | + | 0.986796i | \(0.551784\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.19739 | 0.116853 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.65515 | 0.353357 | 0.176678 | − | 0.984269i | \(-0.443465\pi\) | ||||
0.176678 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.780421 | −0.0747507 | −0.0373754 | − | 0.999301i | \(-0.511900\pi\) | ||||
−0.0373754 | + | 0.999301i | \(0.511900\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.6509 | 1.29569 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.57304 | −0.336123 | −0.168062 | − | 0.985777i | \(-0.553751\pi\) | ||||
−0.168062 | + | 0.985777i | \(0.553751\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.925577 | 0.0863105 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.39595 | 0.313955 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.65755 | 0.151948 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.61879 | 0.874435 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.9418 | 1.88826 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.3561 | 1.45136 | 0.725682 | − | 0.688030i | \(-0.241524\pi\) | ||||
0.725682 | + | 0.688030i | \(0.241524\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.5190 | 1.54246 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.7380 | −1.54978 | −0.774889 | − | 0.632098i | \(-0.782194\pi\) | ||||
−0.774889 | + | 0.632098i | \(0.782194\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.32548 | −0.114934 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.41829 | −0.122067 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.2460 | −1.13168 | −0.565839 | − | 0.824516i | \(-0.691448\pi\) | ||||
−0.565839 | + | 0.824516i | \(0.691448\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.27964 | −0.617451 | −0.308726 | − | 0.951151i | \(-0.599902\pi\) | ||||
−0.308726 | + | 0.951151i | \(0.599902\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.48299 | 0.209106 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.45458 | 0.539759 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.44774 | 0.120229 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.6324 | 1.28934 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.1910 | 1.16257 | 0.581287 | − | 0.813699i | \(-0.302549\pi\) | ||||
0.581287 | + | 0.813699i | \(0.302549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.8909 | −0.967664 | −0.483832 | − | 0.875161i | \(-0.660755\pi\) | ||||
−0.483832 | + | 0.875161i | \(0.660755\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.67737 | 0.620678 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.16275 | 0.495004 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.709493 | −0.0566237 | −0.0283118 | − | 0.999599i | \(-0.509013\pi\) | ||||
−0.0283118 | + | 0.999599i | \(0.509013\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.88642 | −0.625433 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.477410 | −0.0376252 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.2640 | −1.35222 | −0.676112 | − | 0.736799i | \(-0.736336\pi\) | ||||
−0.676112 | + | 0.736799i | \(0.736336\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.5411 | 0.820626 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.82603 | 0.682978 | 0.341489 | − | 0.939886i | \(-0.389069\pi\) | ||||
0.341489 | + | 0.939886i | \(0.389069\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.9794 | −0.844572 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.13930 | −0.469484 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.823790 | 0.0626316 | 0.0313158 | − | 0.999510i | \(-0.490030\pi\) | ||||
0.0313158 | + | 0.999510i | \(0.490030\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.515797 | 0.0389906 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −19.8081 | −1.48887 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.190010 | −0.0142020 | −0.00710100 | − | 0.999975i | \(-0.502260\pi\) | ||||
−0.00710100 | + | 0.999975i | \(0.502260\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.5591 | −1.08217 | −0.541083 | − | 0.840969i | \(-0.681986\pi\) | ||||
−0.541083 | + | 0.840969i | \(0.681986\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.97801 | −0.737596 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.88040 | 0.432336 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.5922 | 1.06708 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.731551 | 0.0532125 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.9084 | −1.58523 | −0.792617 | − | 0.609720i | \(-0.791282\pi\) | ||||
−0.792617 | + | 0.609720i | \(0.791282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.18409 | −0.445140 | −0.222570 | − | 0.974917i | \(-0.571445\pi\) | ||||
−0.222570 | + | 0.974917i | \(0.571445\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.29984 | 0.236306 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.4254 | −1.24151 | −0.620756 | − | 0.784004i | \(-0.713174\pi\) | ||||
−0.620756 | + | 0.784004i | \(0.713174\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.2398 | −1.00943 | −0.504717 | − | 0.863285i | \(-0.668403\pi\) | ||||
−0.504717 | + | 0.863285i | \(0.668403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 18.0016 | 1.26974 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.746742 | −0.0524110 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.02106 | 0.630058 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.21125 | −0.153692 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −11.6688 | −0.807148 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.9263 | 1.50947 | 0.754734 | − | 0.656031i | \(-0.227766\pi\) | ||||
0.754734 | + | 0.656031i | \(0.227766\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.9875 | −1.16396 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.54662 | 0.514675 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.17873 | −0.215786 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.0490 | −1.01692 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.56798 | 0.307276 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.60831 | 0.509490 | 0.254745 | − | 0.967008i | \(-0.418008\pi\) | ||||
0.254745 | + | 0.967008i | \(0.418008\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.38904 | 0.159270 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.536195 | −0.0355885 | −0.0177943 | − | 0.999842i | \(-0.505664\pi\) | ||||
−0.0177943 | + | 0.999842i | \(0.505664\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.1704 | 1.06857 | 0.534286 | − | 0.845304i | \(-0.320581\pi\) | ||||
0.534286 | + | 0.845304i | \(0.320581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.43709 | −0.357734 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.59466 | 0.628567 | 0.314284 | − | 0.949329i | \(-0.398236\pi\) | ||||
0.314284 | + | 0.949329i | \(0.398236\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.06959 | 0.0697727 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.3676 | −0.933276 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 25.1698 | 1.62810 | 0.814048 | − | 0.580798i | \(-0.197259\pi\) | ||||
0.814048 | + | 0.580798i | \(0.197259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.4350 | −0.736591 | −0.368295 | − | 0.929709i | \(-0.620058\pi\) | ||||
−0.368295 | + | 0.929709i | \(0.620058\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.0264 | 1.28469 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.73395 | 0.430216 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.65284 | −0.232425 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −37.1434 | −2.35386 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.0793 | −0.699322 | −0.349661 | − | 0.936876i | \(-0.613703\pi\) | ||||
−0.349661 | + | 0.936876i | \(0.613703\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.20285 | −0.264231 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.46009 | 0.467169 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.82315 | −0.612751 | −0.306376 | − | 0.951911i | \(-0.599116\pi\) | ||||
−0.306376 | + | 0.951911i | \(0.599116\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.03309 | −0.188467 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.45872 | −0.214090 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.01282 | 0.555754 | 0.277877 | − | 0.960617i | \(-0.410369\pi\) | ||||
0.277877 | + | 0.960617i | \(0.410369\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.39722 | −0.208690 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.3410 | −1.91804 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −31.4219 | −1.91583 | −0.957914 | − | 0.287055i | \(-0.907324\pi\) | ||||
−0.957914 | + | 0.287055i | \(0.907324\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7742 | −0.654484 | −0.327242 | − | 0.944941i | \(-0.606119\pi\) | ||||
−0.327242 | + | 0.944941i | \(0.606119\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.70205 | −0.103013 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.54079 | 0.273820 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.6572 | 1.84202 | 0.921008 | − | 0.389544i | \(-0.127367\pi\) | ||||
0.921008 | + | 0.389544i | \(0.127367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.7231 | −0.881448 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.39866 | −0.560677 | −0.280339 | − | 0.959901i | \(-0.590447\pi\) | ||||
−0.280339 | + | 0.959901i | \(0.590447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.4967 | 1.09951 | 0.549757 | − | 0.835325i | \(-0.314720\pi\) | ||||
0.549757 | + | 0.835325i | \(0.314720\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.96555 | −0.353369 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.65304 | −0.274660 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.67295 | −0.392527 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −17.8172 | −1.04446 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.3951 | −0.607288 | −0.303644 | − | 0.952786i | \(-0.598203\pi\) | ||||
−0.303644 | + | 0.952786i | \(0.598203\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.53271 | −0.496794 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.44017 | 0.373696 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.31568 | −0.0760876 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.89253 | −0.224361 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 36.1471 | 2.07660 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.29821 | −0.246115 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6878 | 1.23779 | 0.618894 | − | 0.785474i | \(-0.287581\pi\) | ||||
0.618894 | + | 0.785474i | \(0.287581\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.63188 | 0.434163 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.7859 | 0.895134 | 0.447567 | − | 0.894250i | \(-0.352291\pi\) | ||||
0.447567 | + | 0.894250i | \(0.352291\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.9086 | 0.786160 | 0.393080 | − | 0.919504i | \(-0.371410\pi\) | ||||
0.393080 | + | 0.919504i | \(0.371410\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.23226 | −0.0694301 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.52800 | −0.254318 | −0.127159 | − | 0.991882i | \(-0.540586\pi\) | ||||
−0.127159 | + | 0.991882i | \(0.540586\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.57390 | −0.368068 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.48519 | −0.473597 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.25815 | −0.459496 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.42147 | 0.0788488 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.81169 | 0.100187 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.551694 | −0.0304159 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.9864 | −1.59324 | −0.796618 | − | 0.604483i | \(-0.793380\pi\) | ||||
−0.796618 | + | 0.604483i | \(0.793380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.0485 | −0.769855 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.75453 | 0.423675 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.05627 | −0.220959 | −0.110480 | − | 0.993878i | \(-0.535239\pi\) | ||||
−0.110480 | + | 0.993878i | \(0.535239\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.29456 | 0.450499 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.9838 | −1.51541 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.08393 | −0.382497 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.14866 | −0.115680 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.8017 | 0.901960 | 0.450980 | − | 0.892534i | \(-0.351075\pi\) | ||||
0.450980 | + | 0.892534i | \(0.351075\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.4514 | 0.720037 | 0.360018 | − | 0.932945i | \(-0.382770\pi\) | ||||
0.360018 | + | 0.932945i | \(0.382770\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.01605 | 0.107609 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.1803 | −1.12731 | −0.563656 | − | 0.826010i | \(-0.690606\pi\) | ||||
−0.563656 | + | 0.826010i | \(0.690606\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.31767 | −0.388382 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.84789 | −0.203652 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.2466 | −0.751905 | −0.375953 | − | 0.926639i | \(-0.622684\pi\) | ||||
−0.375953 | + | 0.926639i | \(0.622684\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.3963 | −0.652435 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −22.3294 | −1.17199 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.48265 | −0.339317 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.98613 | 0.155874 | 0.0779372 | − | 0.996958i | \(-0.475167\pi\) | ||||
0.0779372 | + | 0.996958i | \(0.475167\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.5517 | −1.12194 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.75228 | 0.0909737 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7039 | −0.761341 | −0.380671 | − | 0.924711i | \(-0.624307\pi\) | ||||
−0.380671 | + | 0.924711i | \(0.624307\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.32143 | 0.119878 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.05792 | −0.105988 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.3896 | 1.56101 | 0.780503 | − | 0.625151i | \(-0.214963\pi\) | ||||
0.780503 | + | 0.625151i | \(0.214963\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.9695 | −1.94523 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.0848 | −1.53726 | −0.768630 | − | 0.639693i | \(-0.779061\pi\) | ||||
−0.768630 | + | 0.639693i | \(0.779061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.34213 | −0.119366 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.0292 | −0.916476 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.4816 | −1.13986 | −0.569930 | − | 0.821693i | \(-0.693030\pi\) | ||||
−0.569930 | + | 0.821693i | \(0.693030\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.97441 | −0.150422 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.1776 | 2.07713 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.18911 | −0.311408 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.0925 | −0.757469 | −0.378734 | − | 0.925505i | \(-0.623641\pi\) | ||||
−0.378734 | + | 0.925505i | \(0.623641\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.07701 | 0.154043 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.76014 | −0.436374 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 10.4596 | 0.519742 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.7017 | −1.32355 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.9349 | 0.738483 | 0.369241 | − | 0.929334i | \(-0.379618\pi\) | ||||
0.369241 | + | 0.929334i | \(0.379618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.7496 | 1.51676 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.40115 | 0.216566 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0002 | −0.785419 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 16.8992 | 0.827557 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.91475 | −0.240101 | −0.120051 | − | 0.992768i | \(-0.538306\pi\) | ||||
−0.120051 | + | 0.992768i | \(0.538306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.1682 | −0.690516 | −0.345258 | − | 0.938508i | \(-0.612209\pi\) | ||||
−0.345258 | + | 0.938508i | \(0.612209\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.55531 | −0.124243 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.21357 | 0.155881 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.21701 | 0.107289 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.9839 | −0.723428 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.27141 | −0.253915 | −0.126957 | − | 0.991908i | \(-0.540521\pi\) | ||||
−0.126957 | + | 0.991908i | \(0.540521\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.7421 | 0.756517 | 0.378259 | − | 0.925700i | \(-0.376523\pi\) | ||||
0.378259 | + | 0.925700i | \(0.376523\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.36084 | −0.161140 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.37852 | 0.113780 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.2511 | −1.01426 | −0.507129 | − | 0.861870i | \(-0.669293\pi\) | ||||
−0.507129 | + | 0.861870i | \(0.669293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −16.0877 | −0.766082 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.6058 | −0.979012 | −0.489506 | − | 0.872000i | \(-0.662823\pi\) | ||||
−0.489506 | + | 0.872000i | \(0.662823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.5007 | −0.639996 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.9435 | −1.55817 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −28.0196 | −1.32233 | −0.661164 | − | 0.750241i | \(-0.729937\pi\) | ||||
−0.661164 | + | 0.750241i | \(0.729937\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −40.9627 | −1.92886 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 27.6038 | 1.29694 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.733188 | −0.0343724 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5111 | −0.538466 | −0.269233 | − | 0.963075i | \(-0.586770\pi\) | ||||
−0.269233 | + | 0.963075i | \(0.586770\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.55778 | 0.212739 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.58908 | −0.167160 | −0.0835800 | − | 0.996501i | \(-0.526635\pi\) | ||||
−0.0835800 | + | 0.996501i | \(0.526635\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.30656 | −0.339565 | −0.169782 | − | 0.985482i | \(-0.554306\pi\) | ||||
−0.169782 | + | 0.985482i | \(0.554306\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.3064 | −0.663444 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 42.6213 | 1.97228 | 0.986140 | − | 0.165918i | \(-0.0530586\pi\) | ||||
0.986140 | + | 0.165918i | \(0.0530586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.99976 | −0.184692 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.64704 | 0.0758915 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.2676 | −1.57563 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.56977 | −0.117909 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.11611 | 0.371611 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.1882 | −1.56210 | −0.781049 | − | 0.624470i | \(-0.785315\pi\) | ||||
−0.781049 | + | 0.624470i | \(0.785315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.35879 | −0.381128 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.10828 | 0.0504283 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.67511 | −0.348509 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.6718 | −1.16330 | −0.581650 | − | 0.813439i | \(-0.697593\pi\) | ||||
−0.581650 | + | 0.813439i | \(0.697593\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.0773 | 1.81236 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.7593 | 0.530690 | 0.265345 | − | 0.964153i | \(-0.414514\pi\) | ||||
0.265345 | + | 0.964153i | \(0.414514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.65243 | −0.209535 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.8482 | −0.487588 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.77444 | 0.169307 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.1953 | 1.08313 | 0.541566 | − | 0.840658i | \(-0.317832\pi\) | ||||
0.541566 | + | 0.840658i | \(0.317832\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.4890 | −0.915382 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.90898 | 0.441819 | 0.220910 | − | 0.975294i | \(-0.429097\pi\) | ||||
0.220910 | + | 0.975294i | \(0.429097\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5710 | 0.692902 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 25.4880 | 1.13196 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 31.1842 | 1.38221 | 0.691107 | − | 0.722753i | \(-0.257123\pi\) | ||||
0.691107 | + | 0.722753i | \(0.257123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.34373 | 0.147918 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.64469 | −0.160917 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.28758 | 0.144868 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.85681 | −0.213602 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.91237 | −0.0839439 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −43.5489 | −1.90791 | −0.953955 | − | 0.299949i | \(-0.903030\pi\) | ||||
−0.953955 | + | 0.299949i | \(0.903030\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22.4814 | −0.983044 | −0.491522 | − | 0.870865i | \(-0.663559\pi\) | ||||
−0.491522 | + | 0.870865i | \(0.663559\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.19739 | −0.0522583 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.8044 | −0.862695 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1433 | −0.962752 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.3850 | 0.884635 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.8231 | −0.555431 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.65515 | −0.158026 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.441095 | 0.0190346 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −30.5775 | −1.31707 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.3186 | −1.26051 | −0.630253 | − | 0.776389i | \(-0.717049\pi\) | ||||
−0.630253 | + | 0.776389i | \(0.717049\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 33.7979 | 1.45041 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.780421 | 0.0334295 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.1177 | 1.62980 | 0.814898 | − | 0.579604i | \(-0.196793\pi\) | ||||
0.814898 | + | 0.579604i | \(0.196793\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.2686 | 0.438254 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.72037 | 0.158493 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.19233 | 0.135752 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.6509 | −0.579450 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −0.325749 | −0.0138024 | −0.00690120 | − | 0.999976i | \(-0.502197\pi\) | ||||
−0.00690120 | + | 0.999976i | \(0.502197\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.7273 | −0.453715 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.8747 | −1.43019 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.3560 | 1.49008 | 0.745040 | − | 0.667020i | \(-0.232431\pi\) | ||||
0.745040 | + | 0.667020i | \(0.232431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.57304 | 0.150319 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.39503 | −0.226570 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.1728 | 0.594157 | 0.297078 | − | 0.954853i | \(-0.403988\pi\) | ||||
0.297078 | + | 0.954853i | \(0.403988\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.26903 | −0.346048 | −0.173024 | − | 0.984918i | \(-0.555354\pi\) | ||||
−0.173024 | + | 0.984918i | \(0.555354\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 50.8588 | 2.12465 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.925577 | −0.0385992 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.4121 | 0.433462 | 0.216731 | − | 0.976231i | \(-0.430461\pi\) | ||||
0.216731 | + | 0.976231i | \(0.430461\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.3559 | 0.596612 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.25286 | 0.342386 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.4261 | 0.638883 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.39595 | −0.140405 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 35.3519 | 1.45913 | 0.729564 | − | 0.683912i | \(-0.239723\pi\) | ||||
0.729564 | + | 0.683912i | \(0.239723\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.8369 | 0.652547 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 40.4520 | 1.66397 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.6716 | −1.09527 | −0.547636 | − | 0.836717i | \(-0.684472\pi\) | ||||
−0.547636 | + | 0.836717i | \(0.684472\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.65755 | −0.0679530 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 33.0568 | 1.35292 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.1497 | −1.55876 | −0.779378 | − | 0.626554i | \(-0.784465\pi\) | ||||
−0.779378 | + | 0.626554i | \(0.784465\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −37.2826 | −1.52079 | −0.760395 | − | 0.649461i | \(-0.774995\pi\) | ||||
−0.760395 | + | 0.649461i | \(0.774995\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −18.5259 | −0.754434 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.61879 | −0.391059 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.3600 | −0.542266 | −0.271133 | − | 0.962542i | \(-0.587398\pi\) | ||||
−0.271133 | + | 0.962542i | \(0.587398\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.73351 | 0.0702454 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.52039 | −0.0615085 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −26.5021 | −1.07041 | −0.535205 | − | 0.844722i | \(-0.679766\pi\) | ||||
−0.535205 | + | 0.844722i | \(0.679766\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.9418 | −0.844453 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.6828 | 0.752142 | 0.376071 | − | 0.926591i | \(-0.377275\pi\) | ||||
0.376071 | + | 0.926591i | \(0.377275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.4388 | 0.942083 | 0.471042 | − | 0.882111i | \(-0.343878\pi\) | ||||
0.471042 | + | 0.882111i | \(0.343878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.31274 | −0.0526784 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.96364 | 0.278992 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.0883 | 1.08180 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.8971 | −0.753476 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.8401 | −0.949061 | −0.474530 | − | 0.880239i | \(-0.657382\pi\) | ||||
−0.474530 | + | 0.880239i | \(0.657382\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −50.9004 | −2.02311 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.3561 | −0.649070 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.57209 | −0.379260 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.4822 | 0.691587 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −27.4559 | −1.08444 | −0.542221 | − | 0.840236i | \(-0.682416\pi\) | ||||
−0.542221 | + | 0.840236i | \(0.682416\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.7027 | −1.09249 | −0.546245 | − | 0.837626i | \(-0.683943\pi\) | ||||
−0.546245 | + | 0.837626i | \(0.683943\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.5190 | −0.689808 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.42407 | −0.134614 | −0.0673070 | − | 0.997732i | \(-0.521441\pi\) | ||||
−0.0673070 | + | 0.997732i | \(0.521441\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.7453 | 1.52088 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.37920 | 0.289214 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.5176 | 1.27251 | 0.636255 | − | 0.771478i | \(-0.280482\pi\) | ||||
0.636255 | + | 0.771478i | \(0.280482\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.7380 | 0.693082 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.4873 | 0.604219 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 34.5960 | 1.34767 | 0.673834 | − | 0.738882i | \(-0.264646\pi\) | ||||
0.673834 | + | 0.738882i | \(0.264646\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.35365 | −0.0915465 | −0.0457732 | − | 0.998952i | \(-0.514575\pi\) | ||||
−0.0457732 | + | 0.998952i | \(0.514575\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.6043 | −0.411835 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.32548 | 0.0514000 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.34000 | 0.0518849 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −17.6622 | −0.682859 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 19.5173 | 0.753457 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.6612 | −0.912071 | −0.456035 | − | 0.889962i | \(-0.650731\pi\) | ||||
−0.456035 | + | 0.889962i | \(0.650731\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.41829 | 0.0545901 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.3029 | 0.626572 | 0.313286 | − | 0.949659i | \(-0.398570\pi\) | ||||
0.313286 | + | 0.949659i | \(0.398570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.95880 | 0.151925 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.24474 | 0.0476986 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.14519 | 0.120347 | 0.0601737 | − | 0.998188i | \(-0.480835\pi\) | ||||
0.0601737 | + | 0.998188i | \(0.480835\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.2460 | 0.506102 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −37.5385 | −1.43218 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.82903 | 0.183972 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.58626 | −0.136428 | −0.0682139 | − | 0.997671i | \(-0.521730\pi\) | ||||
−0.0682139 | + | 0.997671i | \(0.521730\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.59545 | 0.212553 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.27964 | 0.276133 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.9898 | −1.09807 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.2733 | −0.842455 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.8783 | −0.561945 | −0.280972 | − | 0.959716i | \(-0.590657\pi\) | ||||
−0.280972 | + | 0.959716i | \(0.590657\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.1113 | 0.569933 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.48299 | −0.0935149 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.03150 | −0.302056 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.46752 | 0.167781 | 0.0838906 | − | 0.996475i | \(-0.473265\pi\) | ||||
0.0838906 | + | 0.996475i | \(0.473265\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.7861 | 0.554521 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.70410 | 0.213620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.45458 | −0.241388 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −58.4299 | −2.18210 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.85410 | 0.330202 | 0.165101 | − | 0.986277i | \(-0.447205\pi\) | ||||
0.165101 | + | 0.986277i | \(0.447205\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.69572 | −0.0631520 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 26.5455 | 0.987237 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.44774 | −0.0537678 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.5022 | 0.945823 | 0.472912 | − | 0.881110i | \(-0.343203\pi\) | ||||
0.472912 | + | 0.881110i | \(0.343203\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.1110 | −0.559668 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −24.2516 | −0.896978 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.2118 | 1.33751 | 0.668756 | − | 0.743482i | \(-0.266827\pi\) | ||||
0.668756 | + | 0.743482i | \(0.266827\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −15.6324 | −0.576610 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.2117 | −1.29704 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.4633 | −0.568825 | −0.284413 | − | 0.958702i | \(-0.591799\pi\) | ||||
−0.284413 | + | 0.958702i | \(0.591799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.47983 | 0.311514 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.2279 | −1.80600 | −0.902998 | − | 0.429645i | \(-0.858639\pi\) | ||||
−0.902998 | + | 0.429645i | \(0.858639\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.1910 | −0.519919 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 38.2252 | 1.39859 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.88532 | 0.0688880 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.7967 | 1.26975 | 0.634875 | − | 0.772615i | \(-0.281052\pi\) | ||||
0.634875 | + | 0.772615i | \(0.281052\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.7199 | 0.937286 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.8909 | 0.432753 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0393 | −1.38256 | −0.691282 | − | 0.722585i | \(-0.742954\pi\) | ||||
−0.691282 | + | 0.722585i | \(0.742954\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.75664 | 0.354144 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.8507 | −0.502088 | −0.251044 | − | 0.967976i | \(-0.580774\pi\) | ||||
−0.251044 | + | 0.967976i | \(0.580774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.402539 | −0.0145729 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.67737 | −0.277576 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.1290 | 0.437951 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.18816 | −0.259212 | −0.129606 | − | 0.991566i | \(-0.541371\pi\) | ||||
−0.129606 | + | 0.991566i | \(0.541371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.8038 | 0.821258 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.7005 | −1.14019 | −0.570093 | − | 0.821580i | \(-0.693093\pi\) | ||||
−0.570093 | + | 0.821580i | \(0.693093\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.16275 | −0.221373 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.04112 | 0.252599 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.1821 | 0.830583 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 33.2280 | 1.18899 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.05332 | −0.0733798 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.709493 | 0.0253229 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 52.0064 | 1.85383 | 0.926915 | − | 0.375273i | \(-0.122451\pi\) | ||||
0.926915 | + | 0.375273i | \(0.122451\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.9226 | −0.744866 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.84296 | −0.0655282 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.10977 | 0.216964 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.88642 | 0.279702 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.650091 | 0.0230274 | 0.0115137 | − | 0.999934i | \(-0.496335\pi\) | ||||
0.0115137 | + | 0.999934i | \(0.496335\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.43722 | −0.121600 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.2539 | 1.13963 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 29.4364 | 1.03879 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.477410 | 0.0168265 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 72.9438 | 2.56774 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.529620 | −0.0186205 | −0.00931023 | − | 0.999957i | \(-0.502964\pi\) | ||||
−0.00931023 | + | 0.999957i | \(0.502964\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.69632 | 0.164910 | 0.0824551 | − | 0.996595i | \(-0.473724\pi\) | ||||
0.0824551 | + | 0.996595i | \(0.473724\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.0115 | 0.877191 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.2640 | 0.604733 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.3931 | 0.678478 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.75162 | 0.0612065 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.7904 | 0.620889 | 0.310445 | − | 0.950591i | \(-0.399522\pi\) | ||||
0.310445 | + | 0.950591i | \(0.399522\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.4813 | 0.888221 | 0.444111 | − | 0.895972i | \(-0.353520\pi\) | ||||
0.444111 | + | 0.895972i | \(0.353520\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.5411 | −0.366995 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.3759 | −0.395580 | −0.197790 | − | 0.980244i | \(-0.563376\pi\) | ||||
−0.197790 | + | 0.980244i | \(0.563376\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.15670 | 0.318025 | 0.159013 | − | 0.987277i | \(-0.449169\pi\) | ||||
0.159013 | + | 0.987277i | \(0.449169\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −71.1687 | −2.46881 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.6400 | −0.749783 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.82603 | −0.305437 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.74058 | −0.302119 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.3930 | −1.42904 | −0.714522 | − | 0.699613i | \(-0.753356\pi\) | ||||
−0.714522 | + | 0.699613i | \(0.753356\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.9040 | −0.927726 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.8184 | 0.751464 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.9794 | 0.377704 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.96134 | 0.170474 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −42.9388 | −1.47366 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.44277 | 0.186576 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0489 | −0.891896 | −0.445948 | − | 0.895059i | \(-0.647133\pi\) | ||||
−0.445948 | + | 0.895059i | \(0.647133\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.13930 | 0.209960 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.4390 | −0.595706 | −0.297853 | − | 0.954612i | \(-0.596270\pi\) | ||||
−0.297853 | + | 0.954612i | \(0.596270\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.1349 | 1.81294 | 0.906470 | − | 0.422271i | \(-0.138767\pi\) | ||||
0.906470 | + | 0.422271i | \(0.138767\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.8017 | 0.368121 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.21959 | −0.0415152 | −0.0207576 | − | 0.999785i | \(-0.506608\pi\) | ||||
−0.0207576 | + | 0.999785i | \(0.506608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.823790 | −0.0280097 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.4908 | 0.526095 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.1035 | 0.953345 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.0228 | −0.373493 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.3362 | 0.620585 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.515797 | −0.0174371 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −58.3629 | −1.97077 | −0.985387 | − | 0.170331i | \(-0.945516\pi\) | ||||
−0.985387 | + | 0.170331i | \(0.945516\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.1315 | 0.813935 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.5870 | −0.828357 | −0.414178 | − | 0.910196i | \(-0.635931\pi\) | ||||
−0.414178 | + | 0.910196i | \(0.635931\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −31.9454 | −1.07505 | −0.537525 | − | 0.843248i | \(-0.680641\pi\) | ||||
−0.537525 | + | 0.843248i | \(0.680641\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8081 | 0.665842 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.0532 | 0.908359 | 0.454179 | − | 0.890910i | \(-0.349933\pi\) | ||||
0.454179 | + | 0.890910i | \(0.349933\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.43641 | 0.282948 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −47.4949 | −1.59114 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.74861 | 0.0919789 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.190010 | 0.00635132 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.05425 | 0.101979 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.92208 | 0.297568 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.9172 | 0.363705 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 9.03623 | 0.300707 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.5591 | 0.483960 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.34778 | 0.0447524 | 0.0223762 | − | 0.999750i | \(-0.492877\pi\) | ||||
0.0223762 | + | 0.999750i | \(0.492877\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.1999 | −1.23384 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −54.8993 | −1.81890 | −0.909448 | − | 0.415818i | \(-0.863495\pi\) | ||||
−0.909448 | + | 0.415818i | \(0.863495\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 72.6535 | 2.40448 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.97801 | 0.329863 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.14922 | −0.302134 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.58092 | 0.316045 | 0.158023 | − | 0.987435i | \(-0.449488\pi\) | ||||
0.158023 | + | 0.987435i | \(0.449488\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −50.3468 | −1.65898 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4018 | 0.342380 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.88040 | −0.193346 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.85416 | −0.257965 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.5310 | −0.345512 | −0.172756 | − | 0.984965i | \(-0.555267\pi\) | ||||
−0.172756 | + | 0.984965i | \(0.555267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.3047 | 0.567139 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.6458 | −1.19973 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −14.5922 | −0.477215 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.05730 | −0.132546 | −0.0662731 | − | 0.997802i | \(-0.521111\pi\) | ||||
−0.0662731 | + | 0.997802i | \(0.521111\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −32.2878 | −1.05367 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.4347 | −0.470558 | −0.235279 | − | 0.971928i | \(-0.575600\pi\) | ||||
−0.235279 | + | 0.971928i | \(0.575600\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.34969 | 0.271903 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.731551 | −0.0237974 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −60.1369 | −1.95419 | −0.977094 | − | 0.212810i | \(-0.931739\pi\) | ||||
−0.977094 | + | 0.212810i | \(0.931739\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.21487 | 0.299127 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.5114 | 0.340857 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39.8898 | −1.29216 | −0.646078 | − | 0.763271i | \(-0.723592\pi\) | ||||
−0.646078 | + | 0.763271i | \(0.723592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.9084 | 0.708938 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15.2609 | 0.493313 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.83223 | −0.220624 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.97950 | 0.225145 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.73232 | 0.281395 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.18409 | 0.199073 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −22.2323 | −0.714942 | −0.357471 | − | 0.933924i | \(-0.616361\pi\) | ||||
−0.357471 | + | 0.933924i | \(0.616361\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 19.1707 | 0.615852 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.27517 | −0.233471 | −0.116736 | − | 0.993163i | \(-0.537243\pi\) | ||||
−0.116736 | + | 0.993163i | \(0.537243\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.75482 | −0.120374 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.29984 | −0.105679 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41.3326 | −1.32235 | −0.661173 | − | 0.750233i | \(-0.729941\pi\) | ||||
−0.661173 | + | 0.750233i | \(0.729941\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 61.3040 | 1.95929 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.86446 | −0.0595276 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.54531 | 0.113078 | 0.0565389 | − | 0.998400i | \(-0.481993\pi\) | ||||
0.0565389 | + | 0.998400i | \(0.481993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.4254 | 0.555221 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.28072 | 0.0407658 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.98498 | 0.222109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.4573 | 1.82519 | 0.912596 | − | 0.408863i | \(-0.134075\pi\) | ||||
0.912596 | + | 0.408863i | \(0.134075\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 67.2899 | 2.13538 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.2398 | 0.451433 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.2684 | −1.37032 | −0.685162 | − | 0.728391i | \(-0.740268\pi\) | ||||
−0.685162 | + | 0.728391i | \(0.740268\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.34013 | −0.263870 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8020.2.a.c.1.4 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.4 | ✓ | 28 | 1.1 | even | 1 | trivial |